JP4093861B2 - Compensation of large magnetic errors for electronic compass and all orientation operations - Google Patents

Description

This invention was made with US government support under contract number DAAB07-95-C-M028. The government has certain rights in this invention.
The present invention relates to an electronic compass. In particular, the present invention relates to a technique for compensating an electronic compass for magnetic errors.

  Electronic compass is well known in the art. Typically, this type of device uses a magnetic sensor, such as a magnetic flux gate, to measure the magnetic field to determine the orientation of the earth's magnetic field, i. However, as with a compass with a magnetic needle or direction scale plate (compass), when an electronic compass is used in an environment of ferrous metal or a perturbation field, the magnetic field detected by the magnetometer sensor is disturbed, and the measured value of the earth's magnetic field and An error occurs in the compass magnetic needle azimuth.

  To obtain accurate measurements, it is necessary to compensate for these magnetic perturbations. In order to compensate for a compass with a magnetic needle and direction scale plate, a perturbation field is physically neutralized or offset by using a bar magnet or a soft iron lump. These magnets and soft iron blocks must be carefully placed around the compass so as to cancel out the magnetic perturbations and reduce the deviation error to, for example, 3-5 °. Furthermore, even after such a reduction, it is necessary to plot the residual deviation error against the true direction so that the user can correct the value of the azimuth.

An electronic compass has a configuration in which data passed from a magnetometer sensor is processed by a microprocessor, and compensation can be performed using a numerical solution. One specific example of compensation using numerical solutions is the traditional 5-term compensation formula applied to the level compass. In this compensation formula, the deviation (deviation) of the compass measurement orientation relative to the true orientation is expressed in degrees (°) as a function of the true orientation angle θ. In terms of the formula:
Deviation = A + B · sin (θ) + C · cos (θ) + D · sin (2θ) + E · cos (2θ)
Here, A, B, C, D, and E are coefficients whose values are obtained through the calibration procedure. This compensation technique has certain limitations. For example, the above compensation formula is only an approximation and is effective only when the deviation is small and the values of A, B, C, D, and E are small. Therefore, this compensation technique is used only after the deviation error is reduced by physical compensation such as adding a magnet or a soft iron ingot. Furthermore, the compensation formula is valid only for the level compass, and is not suitable for an environment where the orientation of the compass fluctuates greatly in the three-dimensional space, for example, in a tilted ship. If the latitude changes, the compensation accuracy will be affected. This compensation technique can also be applied to aircraft fluxgate compass, but is only effective for ordinary drooping fluxgate compass because the coefficient depends on tilt orientation and magnetic latitude.

  In general, compensation techniques have been implemented so far, but many of them are limited to a two-axis compass, and sufficient results cannot be obtained when the compass takes various orientations in a three-dimensional space. Some conventional compensation techniques apply to a three-axis compass. However, since this type of prior art relies on a symmetric coefficient matrix, it cannot sufficiently compensate for certain errors.

  To address these and other issues, the present invention uses a three-axis physical model to numerically compensate for magnetic field measurement error in an electronic compass. This model is based on the principle of physics, not approximation, and provides highly accurate compensation. In addition, the model utilizes a linear algebra method that facilitates the application of compensation and parameter determination required for compensation. By using a three-axis physical model, the present invention is not limited to use with a generally horizontal orientation, but compensates the electronic compass for any orientation.

According to one embodiment, the present invention relates to an electronic compass orientation compensation method for compensating an electronic compass so that accurate orientation data can be obtained even under the influence of a perturbation field. For each combination of orientation and orientation, a measured magnetic field vector H _MEAS representing the magnetic field strength for the three axes and a measured gravity vector G _MEAS representing the gravity field strength for the three axes are acquired. By using the system equation based on these measurement vector, calculates a matrix compensation factor L _E and vector compensation coefficients H _PE. Calculated matrix compensation coefficient L _E and vector compensation factor H _PE is used to correct the magnetometer output data measured after, thereby obtaining accurate Earth magnetic field data.

  Other embodiments relate to an electronic compass apparatus and microprocessor readable medium implementing the method of the present invention. The description in this section does not describe all illustrated embodiments or all specific examples of the present invention. These embodiments will be described in more detail with reference to the embodiments of the invention described below and the drawings.

The above and other advantages of the present invention will be made clear in the following embodiments of the present invention made with reference to the drawings.
Various modifications and alternative forms of the present invention are possible. Specific forms are illustrated in the drawings and described below. However, it is not intended that the invention be limited to the specific forms described. On the contrary, the invention is intended to cover all modifications, equivalents, and alternatives falling within the scope of the invention as defined by the claims.

  The present invention is applicable to an electronic compass. The present invention is particularly effective for a compass that operates in various orientations in a poor magnetic field environment with large magnetic perturbations. Various features of the present invention can be understood through the description of various embodiments of the invention.

  The present invention effectively performs accurate compensation and operation in all possible orientations of the compass, which allows the vehicle or device in which the compass is installed to take any orientation. Both “steel” and “soft iron” errors are compensated. Even a fixed magnetic perturbation larger than the geomagnetic field (geomagnetic field) is compensated. Since the magnetic field signal is compensated prior to the calculation of the azimuth by the magnetic field signal, higher accuracy is realized as compared with the conventional technique. Since the compensation formula used in the present invention is based on the physics of the magnetic field and does not require mathematical approximation, the accuracy is further improved.

  Other advantages include compensation for various sensor errors that do not depend on the magnetic field, such as zero offset, unequal scale factor, axis mismatch, and axis mismatch between the magnetometer and orientation sensor, with the same magnetic field compensation formula and calibration procedure. can do.

  According to one specific embodiment of the invention, the electronic compass is based on a three-axis electronic magnetometer that is fixed relative to the vehicle or other device in which it is installed. A triaxial accelerometer or orientation sensor measures the direction of gravity, and a local horizontal plane is defined from which the compass orientation is defined. As will be apparent to those skilled in the art, the direction of gravity may be detected using other configurations, such as an aircraft flight control sensor system. The computer microprocessor uses the values obtained for the measurement magnetic field and the measurement gravitational field to calculate the magnetic orientation of that axis regardless of the compass orientation. As a result, the electronic compass can operate in any orientation and does not need to remain level.

  In order to calibrate the electronic compass, the magnetic field and gravitational field measurements are made in a non-biased distribution with varying pitch, roll and orientation orientation combinations. Next, for each orientation combination, an equation is established that gives an estimate of the earth's magnetic field as a function of the matrix coefficients, vector coefficients and measured magnetic field to be determined. In this way, a system equation (simultaneous equation) is created based on a series of measurements. Some of these equations are linear (linear) and others are quadratic equations. The quadratic equation is reconstructed as an approximated linear equation.

  Next, a subset of the linear equations is first solved to obtain preliminary (initial) estimates for matrix coefficients and vector coefficients. Next, solve all system equations and subdivide the preliminary estimates. All system equations are iteratively solved as necessary, and the estimated values are subdivided to improve the compensation accuracy. The matrix and vector coefficients thus obtained are then stored and stored and used to compensate for magnetometer errors in normal operation of the electronic compass.

In the remainder of this disclosure, the principles underlying the present invention will be described first. Next, measurement value acquisition processing used when the electronic compass is calibrated will be described. Next, a compensation formula used to compensate the electronic compass will be described. Finally, processing for solving a system equation and obtaining a required value for a required numerical coefficient will be described.
Basic Principle As described above, the measurement magnetic field is affected by errors existing in the operating environment, for example, caused by ferrous metal. These errors are caused by additive magnetic perturbations, which causes deviation errors (deviations from true directions) in the direction. Due to these perturbations, the measured magnetic field H _MEAS does not match the geomagnetic field H _{EARTH and} has the following relationship.

Here, H _INDUCED represents an induced magnetic field perturbation, and H _PERM represents a permanent magnetic field perturbation.
The effect of perturbation on the measurement field is shown in FIGS. 1A and 1B for a very simple case of two axes. FIG. 1A shows the trajectory of the geomagnetic field when there is no perturbation assuming a level compass and a 360 ° compass shake. As is clear from FIG. 1A, the locus is a circle, and the azimuth is defined clockwise from magnetic north. H _EARTH rotates counterclockwise with compass deflection, and the vertical (vertical) magnetic field component H _Z is a constant.

FIG. 1B shows the effect of synthesis by H _PERM and H _INDUCED. The center of the locus is shifted by the former, and an elliptical locus is formed by the latter. Accordingly, the trajectory is an ellipse with a center shifted, and can have an arbitrary orientation (direction). Furthermore, the point rotates along the ellipse. If H _PERM is larger than H _EARTH, H _MEAS cannot be shaken, and an error of 180 ° occurs depending on the point. In addition, H _INDUCED perturbation causes H _MEAS to contain a certain deviation error in all directions, making it inaccurate for all orientations.

Permanent magnetic field perturbation H _PERM is based on permanent magnetism and direct current in any part of the compass and its installation environment. Thus, in the case of a compass, the H _PERM is constant and unchanged for the compass and its installation. On the other hand, since H _EARTH changes depending on the orientation, the orientation of H _PERM with respect to H _EARTH changes depending on the orientation of the compass. H _PERM generates a zero offset of the magnetic field for all three axes, resulting in an azimuth deviation error. These errors vary depending on the azimuth and tilt orientation.

The induced magnetic field perturbation H _INDUCED is due to the magnetizable soft iron metal in the environment where the compass operates. H _INDUCED is variable in both size and direction and is proportional to H _EARTH .

Here, K is a matrix similar to magnetic susceptibility.
The induced magnetic field perturbation vector H _INDUCED can always be decomposed into three linearly independent contributions. In terms of the formula:

Where K is a 3 × 3 magnetic susceptibility matrix characterizing H _INDUCED as a function of H _EARTH . The directions of the unit vectors h ₁ , h ₂ , h ₃ along the _three magnetic field components H ₁ , H ₂ , and H ₃ in the magnetic sensor are fixed and orthogonal to each other, and do not depend on the direction of the earth magnetic field H _EARTH . When any of these components reaches the maximum or minimum value due to the change in the H _EARTH orientation, the remaining two components become zero.

The direction of the earth magnetic field H _EARTH itself has three corresponding orthogonal directions indicated by unit vectors e ₁ , e ₂ , e ₃ , and each component of H _EARTH along each unit vector has a maximum value in the positive or negative direction. Become. These maximum values have distinct values denoted k ₁ , k ₂ , k ₃ . The two orthogonal _triples related to H _INDUCED and H _EARTH are independent of each other. The triplet and the maximum value are both estimated and expressed using the magnetic susceptibility matrix K by a technique called the singular value decomposition method or the SVD method.

  That is, K is decomposed into three SVD matrix factors as follows.

Here, h ₁ , h ₂ , and h ₃ are unit column vectors corresponding to the direction of the induced magnetic field in the sensor, k ₁ , k ₂ , and k ₃ are peak values of the respective components, and e ₁ , e ₂ , and e ₃ are the geomagnetic fields H A unit row vector corresponding to the orthogonal component direction for _EARTH . A ternary dyadic representation of K is derived as the sum of three matrices obtained from column vector h> and row vector <e, acting from the left side of H _EARTH .

When K acts on H _EARTH , the above equation becomes

here,

It is.
For any value of K, singular value decomposition of K gives the numerical values for these representations and the respective geometric contributions to H _INDUCED and H _EARTH .

As is well known in the traditional art of physically compensating for non-electronic compass, there are nine independent errors with respect to the induced magnetization perturbation H _INDUCED . Furthermore, there is a specific intensity value for each individual type. In this traditional technique, these various errors are further physically described by “bars” of nine magnetically permeable materials, each arranged in a particular manner around the compass. These virtual bars are equivalent to the distribution of ferrous metal under compass installation and represent this kind of distribution. Actually, the nine types of bars correspond to the nine elements constituting the magnetic susceptibility matrix K. There is no physical law of magnetism that assigns any particular property to the magnetic susceptibility matrix K. For example, the magnetic susceptibility matrix K is not a symmetric matrix that can specify a matrix with only six element values.

  FIG. 2 shows the combined effect of magnetic perturbation due to both permanent and induced magnetic fields on the geomagnetic field trajectory as measured by a three-axis spatial magnetometer. As is well known in linear algebra, a 3 × 3 symmetric matrix defines a three-dimensional ellipsoid with respect to the measured magnetic field magnitude of the sensor, as shown in FIG. However, the asymmetric part in the general matrix causes the locus point along the ellipse to be rotated variously without changing the shape, thereby causing an angular displacement. Therefore, three of the nine types of errors can be described as rotations in the measured magnetic field direction separately from perturbations in the magnetic field strength represented by the ellipsoid. The compass varies considerably due to the error due to this rotation alone, but the error is very similar in other respects.

FIG. 2 shows various examples in which trajectories are simulated for various fixed tilt orientations and magnetic latitudes. For each combination of tilt orientation and magnetic latitude, the trajectory forms a closed planar ellipse corresponding to one section of the ellipsoid in FIG. 2, which is characteristic of the compass and its installation. The center of the ellipsoid is displaced from the origin by the H _PERM vector. In each trajectory, * indicates the measurement magnetic field H _MEAS when the compass direction is north. FIG. 2 illustrates the complexity and difficulty in determining a magnetic perturbation compensation method. There are 12 independent constants related to these characteristics of the compass.

Each type of error can exist independently with any degree of positive or negative intensity in the compass installation environment. In _order to fully compensate the compass error caused by H _INDUCED , nine independent errors must be compensated accurately. Permanent magnetization perturbation H _PERM adds three more errors to be compensated, for a total of 12 errors. The present invention fully and accurately compensates for all types of errors caused by H _INDUCED and H _PERM .

The magnetic susceptibility matrix K is usually small. In the measurement magnetic field H _MEAS , H _EARTH and

Is always in an additive relationship, the permeability matrix M can be used to facilitate the calculation. Here, M has the following relationship with K.

Therefore,

Considering both the induced magnetic field perturbation H _INDUCED and the permanent magnetic field perturbation H _PERM , the magnetic field H _MEAS measured by the magnetometer is expressed by the following equation.

Here, M is a permeability matrix as described above. By determining the values of the matrix M and the vector H _PERM , the compass before compensation can be completely characterized. Except for factors related to parameter instability such as temperature and hysteresis conditions, load shifts and device errors, this equation takes into account almost all errors related to the compass.
EXAMPLE FIG. 3 is a block diagram illustrating an example electronic compass compensation configuration 300 according to one embodiment of the present invention. The electronic compass 300 has a three-axis magnetometer 302 that is fixed relative to the vehicle or device in which it is installed. As shown in FIG. 4, the magnetometer 302 measures a magnetic field in a three-axis internal coordinate system. In FIG. 4, the internal coordinate system of the electronic compass is represented by an X axis, a Y axis, and a Z axis, and is illustrated in comparison with a ground plane orthogonal to the gravity vector G. Usually, but not necessarily, the Z-axis of the internal coordinate system is taken downward with respect to the device on which the compass is installed. The Y-axis is orthogonal to the Z-axis and extends to the right, the X-axis is orthogonal to the Y-axis and Z-axis, and is generally in the “front” direction of the compass and device. The X axis is particularly meaningful, and the azimuth is determined by the orientation of the X axis relative to the earth's magnetic north. Specifically, the angle measured from the north direction to the X-axis direction determines the direction. This angle is defined in the horizontal plane. If the compass is not horizontal and is placed at a certain pitch or roll angle, the azimuth is defined by projecting the X axis onto the horizontal plane. Thus, the magnetic azimuth is an angle measured from the horizontal component of the geomagnetic field to the horizontal component of the X axis of the internal coordinate system related to the compass. This angle is positive when measured clockwise from magnetic north.

  The magnetometer 302 supplies magnetic sensor data to a microprocessor 304 that is responsible for all calculations. The microprocessor 304 stores the generated compensation data in the memory 306 and later retrieves the data from the memory 306 and uses the measured magnetometer data to compensate for magnetic errors. Gravity sensor 308 provides microprocessor 304 with information regarding the orientation of electronic compass 300. This orientation data along with the magnetometer data is used to calibrate the electronic compass 300. The gravity sensor 308 is realized by, for example, a three-axis accelerometer or an orientation sensor. Instead, orientation data may be acquired using external information. For example, if the electronic compass 300 is installed in an aircraft, orientation data can be acquired using an aircraft flight control or navigation system, and a dedicated gravity sensor is not required. After calibrating the electronic compass 300, the compensation data is used to compensate for magnetic errors in the magnetometer measurement data, thereby enabling accurate calculation of the magnetic orientation.

  FIG. 5 shows a specific configuration example of the electronic compass 300 outlined in FIG. The magnetic sensor 502 configured by a magnetoresistive (MR) bridge acquires magnetic field measurement values for each of the three axes that define an internal coordinate system as illustrated in FIG. The MR bridge is particularly suitable for realizing the magnetic sensor 502 with a small size and low power consumption. The magnetic sensor 502 is fixed with respect to the vehicle or device where the electronic compass is installed. The measurement signal is supplied to the sensor electronics module 504. The sensor electronics module 504 can also be implemented, for example, by a well-known common type of sensor processing circuit. The output of the sensor electronics module 504 is fed to a multiplexer 508 that selects each module output in turn.

  In the specific configuration example shown in FIG. 5, the multiplexer 508 also receives acceleration information from the accelerometer 514. These accelerometers 514 measure acceleration and gravity along each of the three axes that make up the internal coordinate system of the electronic compass.

  The multiplexer 508 supplies the magnetic sensor and accelerometer signals to an analog / digital (A / D) converter 518 where the signals are converted to digital data, the converted data being a microprocessor device having a microprocessor 522 and a memory 523. 520. Microprocessor unit 520 uses this information to calculate the azimuth angle. However, since there is a magnetic error, an accurate orientation cannot be obtained without compensation.

  To correct the measurement magnetic field, the microprocessor 522 processes the data according to software 524 loaded into the associated memory 523. The software 524 realizes various routines for calibrating the electronic compass 300, performing magnetic compensation after the electronic compass 300 is calibrated, and calculating the magnetic orientation after performing the magnetic compensation. As a result of the compensation process, the microprocessor 522 calculates an azimuth angle, and the calculated azimuth angle is output to the user via, for example, an ordinary RS-232 data interface.

The physical model equation is used to determine the geomagnetic field H _EARTH from the measured magnetic field H _MEAS.

The magnetic error is compensated using the algebraic inverse of. This algebraic reciprocal is:

The format of the coefficient is changed slightly according to the following definition.

Therefore, the above equation is as follows.

In this equation, _{_EARTH} is a goal to be obtained and represents an accurate estimated value (estimated value) regarding the geomagnetic field (true geomagnetism) calculated in real time from the magnetometer output H _MEAS . Matrix L _E and vector H _PE is compensation coefficient. By determining the numerical values of these compensation factors, it is not necessary to calculate the parameters M and H _PERM of the original model.

Once L _E (matrix compensation factor) and H _PE (vector compensation factor) are determined, the above equation is valid for any orientation in 3-axis space and the electronic compass should be used as a complete 3-axis compass. Can do. This formula (compensation formula) is based on a physical model, and since no approximation is used in the process of deriving this compensation formula, it is effective for any magnitude of magnetic perturbation and any magnitude of the geomagnetic field. It is. Furthermore, the compensation formula depends only on H _MEAS and does not require any external information such as information on the geomagnetic field, gravity vector, local horizontal surface, etc. Once the compass is calibrated, it can be used anywhere in the world regardless of the magnetic latitude.

In compensation type according to the present invention, 9 elements of the matrix L _E is required to sufficiently compensate known in the prior as discussed above techniques, nine related to H _Induced and magnetic susceptibility K of the error It is a numerical value. Further three sets constituting the vector H _PE is a value required to compensate for the H _PERM. Therefore, by setting an appropriate value for these 12 elements, the compensation equation can compensate for all kinds of errors caused by the perturbation field.

As mentioned for the matrix K, no particular properties said to feature the matrix L _E. That is, the matrix L _E is not symmetrical, other, not blessed with properties such as to reduce the number of independent variables needed to fully compensate all 9 types of errors. In the conventional technique for compensating an electronic compass, often but approximation is performed in the equivalent assumes that only a matrix value of the six elements A fitting procedure matrix L _E symmetry of this kind is identified is there. In other cases, further assumptions were added to further reduce the number of coefficients to be determined, for example, four. Its purpose was to simplify the algebraic operations involved in the calibration procedure. According to today's microprocessors and memories, the motivation for simplification once meaningful was lost. Or equal to assume a symmetric matrix for L _E, compensation method as further performs simplification can not compensate for all nine errors related to H _Induced perturbation. This kind of compensation method is incomplete. The present invention provides a method for determining the nine numbers constituting the compensation coefficient matrix L _E, fully compensates for the total error.

In L _E is 3 × 3 matrix, since H _PE is 3-axis vector, to compensate for the compass using the compensation expression, it is necessary to determine the twelve real value elements constituting the compensation factor. Compensation accuracy depends on coefficient accuracy. Therefore, it is particularly beneficial to obtain an accurate coefficient value.

The compensation factor value is determined using any of various calibration procedures. It is preferable to use the internal coordinate system of the compass as the reference coordinate system in the formulated calibration and give priority to the viewpoint of the sensor over the user's earth coordinate system. The internal coordinate system of the compass is indicated by axes in the X, Y, and Z directions in FIG. In this coordinate system, both the geomagnetic field vector H _EARTH and the gravity unit vector G having a constant magnitude constitute a rigid pair forming a constant angle therebetween. These vectors can take any orientation with respect to the X, Y, and Z axes that make up the only coordinate system used. Thus, the Earth coordinate system is not required in the calibration procedure.

FIG. 6A is a flowchart illustrating an exemplary compensation method for compensating an electronic compass, according to yet another embodiment of the present invention. Compensation occurs during normal operation of the electronic compass. First, starting from block 602, a three-axis magnetic field vector H _MEAS and a three-axis gravity vector G _MEAS are measured. Next, at block 604, compensation coefficient i.e., searches the matrix coefficients L _E and vector coefficients H _PE from the memory of the electronic compass 300. These compensation coefficients are acquired by a method as illustrated in FIG. 6B below, for example. In block 606, the compensation equation using the search value for the matrix coefficients L _E and vector coefficients H _PE

Apply. By applying this compensation formula, the magnetic error of the magnetometer data is corrected. A magnetic orientation is calculated at block 608 based on the corrected magnetometer data. The flow then returns to block 602 and repeats the process.

  Compensating the electronic compass 300 in this manner allows the compass to be used in any orientation. Furthermore, the total magnetic error can be compensated even if the magnetic perturbation is greater than the earth's magnetic field. FIG. 10 illustrates the effectiveness of the present invention in compensating for very large magnetic perturbations.

  However, in order to compensate the electronic compass 300, it is necessary to calibrate the compass in advance. Calibration is compensated

In the values of the matrix coefficients using L _E and vector coefficients H _PE intended to include processing of determining, it is sufficient to perform from time to time. FIG. 6B shows an example calibration method for calibrating an electronic compass. Beginning at block 652, calibration measurements, ie, a 3-axis magnetic field vector H _MEAS and a 3-axis gravity vector G _MEAS, are obtained for the selected orientation and orientation combination. In each set of measurements, the vectors H _MEAS and G _MEAS are represented by unit vectors x, y, and z corresponding to the X, Y, and Z axes constituting the compass coordinate system, respectively. In the specific configuration example, the measurement is performed on a set of four orientations (combinations of pitch and roll) for each of four orientations such as north, east, south, and west shown in FIG. It becomes a kind. Note that it is not necessary to select a specific azimuth angle, and it is sufficient that the azimuths are approximately 90 degrees apart. For example, selecting the orientations corresponding to northwest, northeast, southeast, and southwest will work equally well. The same tilt orientation may be used in each orientation. For example, as a set of orientations, a combination of up / down pitch angles and left / right roll angles, i.e., up / left, up / right, down / left, down, under conditions where the pitch angle and roll angle are all about 30 °. / Right can be used. As with the azimuth angle, the pitch angle and roll angle do not matter. Furthermore, the calibration procedure is completely independent of the order of measurement. However, the compass must be kept stable during the measurement to ensure accurate measurement and calibration, especially for G. Calibration accuracy can be improved by measuring the azimuth, pitch, and roll angle with an unbiased distribution (with a substantially uniform distribution). In other embodiments, 24 or 32 different measurement sets are used. The calibration measurement is then stored in the memory of the electronic compass 300 at block 654.

Next, using the 16 measurement sets obtained in this way, that is, the triple vector H _MEAS and the triple vector G _MEAS measured for each of the 16 pitch and roll angle combinations, a simultaneous equation is established. Solving it, L _E and _HPE are determined as shown in block 656 of FIG. 6B. For each measured value H _MEAS in the calibration measurement set,

Is given. Furthermore, through all measurements, _{_EARTH} is constant, but its magnitude and slope are unknown. These properties lead to the system equations used to calculate the coefficients.
First, _{_EARTH} has a certain magnitude (absolute value) H ₀ . Therefore, the square of the size is also a constant.

By combining this equation with the above equation for each measurement set, the following equation is obtained for each value of the recorded calibration measurement set.

Here, H ₀ ² is an unknown constant and represents the square (square) of the magnitude of the geomagnetic field. If a total of 16 types of measurements are performed, a total of 16 equations having the above format are obtained. The value of G _MEAS is not used for this simultaneous equation. These equations are quadratic for the unknown coefficients L _E and H _PE.

  Second, since the tilt angle is constant, the following equation holds for the vector inner product of all measurements.

Here, H _GRAV represents the vertical component of the geomagnetic field with an unknown constant whose value does not change throughout all measurements. Therefore, the following equation holds for each measurement.

Similarly, if 16 types of measurements are performed in total (as a measurement set), 16 vector equations having the above format are obtained. These equations are first order for unknown coefficients. In summary, 16 quadratic equations and 16 linear equations

Constitutes a system equation consisting of 32 equations, including 14 unknowns 9 elements L _E , 3 sets of H _PE and H ₀ and H _GRAV , 96 known measured quantities As a result, three sets of H _MEAS and three sets of G _MEAS are included every 16 measurements. These equations are homogeneous for the unknowns, and there are no error-free constant source values that can be substituted for H ₀ ² and H _GRAV . The ratio of H ₀ to H _GRAV is important, but not the size of each. Therefore, by appropriately normalizing the quantities H ₀ ² , G _MEAS , and unknown coefficients, the unknowns can be reduced from 14 to 13.

Before proceeding to the solution of the system equations, the 16 measurements for H _MEAS and G _MEAS are not necessarily necessary, but only an example. Taking a smaller or larger number of measurements will not conflict with the present invention, but will affect the accuracy of the calibration. For example, if 24 or 32 types of measurements are performed as a set, the accuracy is considerably improved.

The solution of the system equation will be described. First, the system equation is reconstructed into a set of linear equations (simultaneous linear equations). That is, H _EARTH estimated from each measurement is rotated to the north / east / bottom reference system. This rotation uses an initial estimate of the coefficient values and three new parameters to generate 16 system equations for each of the north, east, and bottom components, for a total of 48 equations.

Specifically, the following equation is used to rotate the estimate H _EARTH to the north / east / down reference frame.

Here, R1 (θ) and R2 (φ) are derived from each G _MEAS value, and H _MEAS is a corresponding magnetometer output value. ψ is derived from each G _MEAS value, and H _MEAS is the corresponding magnetometer output value. ψ is a quantity calculated such that H _EAST is zero in each measurement. The above equation is a first order for the unknowns H _EARTH, L _E and H _PE. Subset of 16 equations for H _DOWN is the same as the subset that was used for _{H GRAV = G MEAS '· _} EARTH before.

Of these equations, the 16 “down” equations are truly linear with respect to the unknown coefficients H _DOWN , L _E , and H _PE and are solved for these values by existing standard algorithms. Can do. For convenience, these 16 equations will be collectively referred to as the A equation. All sets of 48 equations (all system equations) including the A equation are also collectively referred to as the B equation. The values of L _E and H _PE are first obtained by solving the A equation, and then the values of L _E and H _PE are subdivided by solving the large B equation.

In performing calibration of the compass, one measure of the H _MEAS and G _MEAS is known by measurement, the compensation coefficient L _E and H _PE is unknown. Record H _MEAS and G _MEAS pairs for each of the 16 measurements.

As described above, the compensation equation that these equations should satisfy is as follows.

Here H _E represents the unknown magnetic field of the Earth, the same throughout the entire measurement. H _E is a fixed vector in the Earth coordinate system, but when viewed from the internal coordinate system, the value of H _E varies with each measurement because it takes various orientations during calibration.

In order to construct a system equation to be solved for the unknown compensation factor, a total of 16 equations are established, one for each H _MEAS and G _MEAS measurement. However, these equations need to be reconstructed appropriately to match standard numerical solutions. As a result, all unknowns become elements of the column vector, and this is multiplied by a system matrix having a large known value. Reconfiguration is performed in the following steps.

For example, 16 linear equations can be obtained by taking the vector inner product of G _MEAS and H _E. The result of the vector dot product is the vertical component of the geomagnetic field, or _HGRAV , which is unknown but is the same throughout all measurements. This equation is written as:

Next, the matrix L _E can be expressed as follows by the three column vectors.

And the above system equation for H _GRAV is as follows for any pair of measured H _MEAS and G _MEAS .

This is a scalar equation because the H _{GRAV on} the right side is simply a numerical value, not a vector. The first product regarding the left side of the G _MEAS (product) becomes a row vector since it is the product of the respective G _MEAS and three columns L _E, applied to a column vector is a H _M was measured.

Reconstructing this equation to collect all unknowns into one long column vector results in the following equivalent form:

The row vector on the left side contains all measured values and differs for each measurement. The column vector on the right side, denoted by P, consists of all unknown compensation coefficients and is common to all measurements. All are 13 sets of vectors. The zero on the right side is a single element, not a vector.

This equation can be simply written as follows, where P is a coefficient vector to be determined, and A is a row vector composed of measured values.

Rewriting this equation for each of a total of 16 measurements with different orientations for each measurement due to the calibration procedure, the A vector becomes a large 16 × 13 system matrix with one row added for each measurement. This system is called the A system equation and is linear (linear) with respect to unknowns. Solve this A system for coefficients. However, since A system is not the whole system, it does not give a complete solution. A system alone can only provide a first order approximation.

To construct the whole system equation, it is necessary to add the square of the magnitude (absolute value) of H _E or the horizontal and north components of H _E to the vector P, as in the method described above. For a large system of objectives, formulate the entire system equation with the 14th element added to the P vector by using the same steps as described for the A system. Thus, the system constructs 32 equations including 14 unknowns.

As described above, each H _E north, east, may be rotated in the components below, these components by the rotation becomes the last three sets of P vectors, a total of 15. Thus, the entire system consists of 48 equations including 15 unknowns. All of these alternative system equations have been proven as calibration calculations to determine the compensation factor.

When finding a solution for the vector P, the element value is rewritten to a compensation coefficient and an appropriate component of the earth's magnetic field. That is, the three rows of the matrix L _E the first nine values of the vector P, rewritten the next three sets in vector H _PE. The remaining elements are rewritten to appropriate values for the geomagnetic field components, but the specific components that are applicable depend on the calculation method and system equations used.

  Furthermore, the order in which the measurement results are incorporated into the system (or used in the system) does not make any difference in the resulting solution. This is a very significant practical advantage and the order of measurement results taken into the calibration procedure does not matter.

As a further advantage of this calibration procedure, no information needs to be added other than the paired measurements H _MEAS and G _MEAS . That is, it is not necessary to give numerical information regarding the pitch, the tilt angle of the roll, and the azimuth angle to the system equation when measurement is performed. Further, there is no need for a compass test range for calibration, and even one aiming in a known orientation is not necessary.

  In a specific example configuration of the present invention, a computer language such as MATLAB, available from Math Works Inc., is used to solve the "A" and "B" system equations. According to this configuration example, the singular value decomposition (SVD) method is used as follows to solve both systems. Attached to the present disclosure is an appendix containing additional workable material, which details the method of performing the calibration calculation. Here is a list of MATLAB® programs that can be used in prototyping these algorithms.

A ・ P = 0 ＋ δ
When N simultaneous linear equations including M unknowns are written in a matrix format, the system matrix A becomes an N × M matrix, and P becomes a column vector of M elements representing M unknowns. In an incapable system, i.e. a system where N> M, matrix A is not a square matrix, the reverse does not exist, and there is no unique solution for P. Therefore, when the matrix product A · P is taken, an N-element column vector is generated as a residual at best.

To find the optimal solution for the vector P a (best solution), specific to SVD analysis, | [delta] | solving the above system equation (simultaneous equation) using least squares to minimize ^2.
The singular value decomposition (SVD) of the non-square matrix A is a factorization into three matrices U, S, and V, and is expressed as follows.

Here, S is a singular value matrix, and the upper left M × M square block is a diagonal matrix. Some of these singular values may be zero. U and V are square and orthogonal matrices, that is, unitary matrices. That is, U ′ · U≡I _N and V ′ · V≡I _M. Various existing numerical software analysis methods can be arbitrarily used to calculate these three matrices. Once these matrices are computed, from the smallest singular value, the last element S _MM (in normal order) of the matrix S, and the Mth column vector of the matrices U and V, the complete least squares for the unknown P A solution is obtained. That is, the residual value σ based on the minimum square sum of squares (RSS) is given by the following equation.

σ≡S _MM
The solution vector P for the unknown is defined as follows.

That is, the Mth column of the SVD matrix factor V. The solution vector P is an M × 1 column vector, and can be normalized again as appropriate. Finally, the residual δ in the equation is an N × 1 vector proportional to σ and is defined by

The other element values of the U, S, and V matrices are meaningless and are discarded.
By analyzing the solution vector determining the values of matrix coefficients L _E and vector coefficients H _PE. That is, the components of the solution vector P are read into the element values of L _E , H _PE , H _NORTH , H _EAST , and H _DOWN . This way, the matrix coefficients L _E and vector coefficients H _PE is determined, the calibration of the electronic compass is completed. In a specific configuration example, by solving iteratively the "B" system obtains a more accurate coefficient L _E and H _PE. FIG. 8 shows the convergence with the number of iterations together with the minimum singular value.

It was observed that the “east” equation contains zero as the solution and the residual is small. Thus, in another specific example configuration, convergence is effectively improved by eliminating these “east” equations from the “B” system. In this example configuration, the “B” system is redefined as a 32 × 14 system where H _NORTH and H _{DOWN that} are part of the solution set are unknown quantities. First solved "A" system of 16 equations involving thirteen unknowns out an initial estimate of the coefficient L _E and H _PE with. Then these results, obtaining 32 consisting equation "B" value applied subdivided for L _E and H _PE system containing 14 unknown quantities. Then, to further subdivide the L _E and H _PE solves the "B" system again. In this configuration example, as shown in FIG. 9, sufficient convergence can be obtained by performing the iterations twice.

In another embodiment of the present invention, it led to the alternate set of equations from the measurement results to determine the L _E and H _PE. As described above, for each measurement, the estimated value _ _EARTH of the geomagnetic field vector is given by

Alternative equations can be established from other equivalent fundamental properties of the geomagnetic field. That is, the vertical and horizontal (north) components of H _EARTH are constant throughout all measurements. Since the vertical component is constant, the vector dot product

, H _GRAV is an unknown constant. Summarizing these equations for each of the 16 measurements gives the following system equation (simultaneous equations):

  The following equation is derived for each of the 16 measurements from a constant horizontal (north) component.

Here H _NORTH is an unknown constant.
Thus, a system consisting of 32 equations is defined. In order to solve these equations for the values of L _E , H _PE , H _GRAV , and H _NORTH , for example, a computer-implemented numerical solution is used. equation

Is first-order (linear) for the unknown coefficients and is solved first. equation

Requires an initial estimate of L _E and H _PE to calculate the horizontal component. Rotation is calculated for G _{MEAS in} the same manner as described above for calculation when rotating the estimated H _EARTH to the north / east / bottom reference coordinate system.

  Next, all equations are solved as if they were a single system consisting of 32 linear (linear) equations. The equations are solved in much the same way as described for the “A” and “B” systems. That is,

The first 16 equations of the form are first solved to obtain preliminary estimates of L _E and H _PE , and then used to solve large system equations to obtain new estimates for L _E and H _PE . Then again further subdivided estimates of L _E and H _PE solving a large system equations. It was observed that only two iterations _yielded sufficiently convergent values for H _GRAV and H _NORTH . After the calibration calculation is complete, the resulting compensation factor is stored in memory 532 as shown in block 658 of FIG. 6B.

Returning to FIG. 6A, in the normal operation of the compass, measurements are taken continuously and repeatedly for H _MEAS and G _MEAS as shown in block 602. After retrieving the value of the compensation coefficient L _E and H _PE from memory at block 604 and proceeds to block 606, to correct the measured output data of the magnetometer determine an accurate azimuth data These compensation coefficients. That is,

Wherein the matrix compensation factor by applying L _E and vector compensation factor H _PE to the a target from the measured output data H _MEAS magnetometer, obtain an estimate (estimated value) _ _EARTH true earth magnetic field (true geomagnetism) To do.

  By compensating the electronic compass as described above, the electronic compass can be used in an arbitrary orientation. In addition, all magnetic errors, including magnetic perturbations greater than the earth's magnetic field, are compensated.

Other advantages are certainly recognized in the calibration method (compensation method). That is, besides compensating for magnetic errors, the compensation method also accurately compensates for various types of sensor errors associated with magnetometer sensors. For example, the bias offset of the sensor is quite similar to the permanent magnetic field perturbation, are recorded in H _PE coefficient (woven). Other magnetometer sensor error, for example, unequal scale factor, consistent and non-orthogonality of the axes, and mismatch such axes of the magnetometer and accelerometer are exactly the same as the induced magnetic field perturbation, it is recorded in L _E Factor ( Woven). All such errors are fully and accurately compensated by the compensation method and calibration procedure of the present invention.

  The various embodiments described above are for illustrative purposes only and do not limit the invention. It will be apparent to those skilled in the art that the exemplary embodiments and applications illustrated and described herein are not strictly followed, and do not depart from the spirit and scope of the invention as set forth in the claims. Various modifications and changes can be made to these embodiments. For example, the value of the compensation factor can be continuously updated while the compass is in use. In addition, various filters, such as Kalman filters, can be used in the calibration process.

FIG. 1A shows the trajectory of the geomagnetic field in a horizontal plane without perturbation. FIG. 1B shows the combined effect of magnetic perturbations due to both permanent and induced magnetic fields as measured by a magnetometer on the geomagnetic field trajectory. Fig. 4 shows the combined effect of magnetic perturbation by both a permanent magnetic field and an induced magnetic field on a geomagnetic field trajectory as measured by a three-axis magnetometer. 1 is a block diagram illustrating an electronic compass compensation configuration according to one embodiment of the present invention. FIG. The local earth coordinate system is shown with the coordinate system of the electronic compass of FIG. It is a block diagram which shows the specific structural example of the electronic compass of FIG. 3 based on another embodiment of this invention. FIG. 6A is a flowchart illustrating an exemplary compensation method for compensating an electronic compass, according to yet another embodiment of the present invention. FIG. 6B is a flowchart illustrating an example calibration method for calibrating an electronic compass according to yet another embodiment of the present invention. Fig. 4 illustrates an example orientation set for use in calibrating an electronic compass, in accordance with certain embodiments of the present invention. 2 is two graphs showing the minimum singular value and convergence for a numerical compensation coefficient solution set obtained using a calibration method, in accordance with certain embodiments of the present invention. FIG. 6 is two graphs showing minimum singular values and convergence for a solution set of numerical compensation coefficients obtained using a calibration method according to another specific embodiment of the present invention. Fig. 6 illustrates the effect of electronic compass accuracy by numerical compensation performed using a compensation method according to an embodiment of the present invention.

Claims (10)

A triaxial magnetometer that provides a measured magnetic field vector H _MEAS representing the magnetic field strength for the three axes for each of a plurality of combinations of orientation and orientation ;
A three-axis gravity sensor that provides a measured gravity vector G _MEAS representing the strength of the gravitational field about three axes for each of a plurality of combinations of orientation and orientation ;
A processor communicatively coupled to the three-axis magnetometer and the three-axis gravity sensor device;
The processor calculates a matrix compensation coefficient L _E and a vector compensation coefficient H _PE as a function of a plurality of measured magnetic field vectors H _MEAS and a plurality of measured gravity vectors G _MEAS by solving a system equation ,
Wherein the processor uses a matrix compensation coefficient L _E and vector compensation coefficient H _PE, the following equation,

To correct the measured magnetic field data and calculate orientation data as a function of the corrected magnetic field data, where _{_EARTH} is the compensation value for the true geomagnetic field,
The matrix compensation coefficient L _E comprises an element for compensating the error associated with the induced magnetic field perturbation and magnetic susceptibility matrix,
The vector compensating factor H _PE includes elements to compensate for the permanent magnetic field perturbation,
Electronic compass device. The processor and coupled, further comprising a memory for storing the matrix compensation coefficient L _E and the vector compensating factor H _PE, electronic compass system of claim 1. 2. The electron according to claim 1 , wherein the plurality of measurement magnetic field vectors H _MEAS and the plurality of measurement gravity vectors G _MEAS are measured in four orientations for each of four directions, and the four directions are 90 degrees apart. Compass device. The four orientations for each of the four orientations are: (i) the first orientation is characterized by an upper pitch angle and a left roll angle, and (ii) the second orientation is characterized by an upper pitch angle and a right roll angle. 4. The electronic compass of claim 3 , wherein (iii) the third orientation is characterized by a lower pitch angle and a left roll angle, and (iv) the fourth orientation is characterized by a lower pitch angle and a right roll angle. apparatus. The electronic compass device according to claim 4 , wherein each pitch angle and each roll angle is 30 ° . The system equation includes a plurality of equations having the following form:

Where H ₀ is the magnitude of _{_EARTH} , and includes a plurality of equations having the form

Here H _GRAV is a constant representing the unknown vertical component of _ _EARTH,
The electronic compass apparatus according to claim 1 . The electronic compass apparatus according to claim 1 , wherein the processor further derives a total system equation by rotating _{_EARTH} to a reference north / east / down coordinate system for each of the plurality of measured magnetic field vectors H _MEAS . The system equation has a first subset of linear equations to be solved for pairs of the measuring magnetic field vector H _MEAS and the measured gravity vector G _MEAS, electronic compass system of claim 1. The processor further comprises:
Estimates and the estimated value of the vector compensating coefficient H _PE of the matrix compensation coefficient L _E calculated by solving the first subset of said linear equations,
Computing the matrix compensation coefficient L _E and the vector compensating coefficient H _PE by solving the whole system equation using the estimated value and the estimated value of the vector compensating coefficient H _PE of the matrix compensation coefficient L _E,
The electronic compass apparatus according to claim 8. Further, the processor is said to improve the computational value of the matrix compensation coefficient L _E and the vector compensating coefficient H _PE by solving the system equations in an iterative process, the electronic compass according to claim 9.

Images